The pair previously exchanged words during the second half at the bet365 Stadium when Mourinho appeared to enter Hughes' technical area, before tempers appeared to be calmed.
But Mourinho walked straight past Hughes at full-time and did not entertain the possibility of a handshake with the former United star, who has had similar problems with Manuel Pellegrini and Tony Pulis in the past.
"It [the handshake] didn't happen," Hughes told BBC Sport. "I seem to get involved in handshake issues!
"I'm not sure why he didn't want to shake my hand, I didn't think there were any issues.
"There was a time he came into my technical box and I told him to get out but that was it. Maybe that was what upset him."
Mourinho was rather less open about the situation, however.
He said: "I prefer not to answer question about handshakes - it's a bad question. It makes it look like it's my fault but that's not right."